Problem: Rewrite as a simplified fraction. ${0.9\overline{93} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 993.9393...\\ 10x &= 9.9393...\end{align*}}$ Subtracting the two equations, we have: ${990x = 984}$ ${x = \dfrac{984}{990}} $ ${x = \dfrac{164}{165}} $